Clifford Dressed Time-Dependent Variational Principle

Abstract

We propose an enhanced Time-Dependent Variational Principle (TDVP) algorithm for Matrix Product States (MPS) that integrates Clifford disentangling techniques to efficiently manage entanglement growth. By leveraging the Clifford group, which maps Pauli strings to other Pauli strings while maintaining low computational complexity, we introduce a Clifford dressed single-site 1-TDVP scheme. During the TDVP integration, we apply a global Clifford transformation as needed to reduce entanglement by iteratively sweeping over two-qubit Clifford unitaries that connect neighboring sites in a checkerboard pattern. We validate the new algorithm numerically using various quantum many-body models, including both integrable and non-integrable systems. Our results demonstrate that the Clifford dressed TDVP significantly improves entanglement management and computational efficiency, achieving higher accuracy, extended simulation times, and enhanced precision in computed observables compared to standard TDVP approaches. Additionally, we propose incorporating Clifford gates directly within the two-site 2-TDVP scheme.

7 pages, 3 figures

References in corpus (39)

• The density-matrix renormalization group in the age of matrix product states
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Efficient simulation of one-dimensional quantum many-body systems
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Improved Simulation of Stabilizer Circuits
• Evolution of Entanglement Entropy in One-Dimensional Systems
• The ITensor Software Library for Tensor Network Calculations
• Time-dependent variational principle for quantum lattices
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Stim: a fast stabilizer circuit simulator
• Stabilizer Rényi entropy
• Entanglement dynamics after quantum quenches in generic integrable systems
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Quantifying nonstabilizerness of matrix product states
• Stabilizer entropies and nonstabilizerness monotones
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Scalable measures of magic resource for quantum computers
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Emergent irreversibility and entanglement spectrum statistics
• Stabilizer entropies are monotones for magic-state resource theory
• Nonstabilizerness via matrix product states in the Pauli basis
• Phase transition in magic with random quantum circuits
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Non-stabilizerness versus entanglement in matrix product states
• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Entanglement-magic separation in hybrid quantum circuits
• Transitions in Entanglement Complexity in Random Circuits
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• Time-dependent variational principle with controlled bond expansion for matrix product states
• Hybrid Stabilizer Matrix Product Operator
• Magic of Random Matrix Product States
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Random unitaries, Robustness, and Complexity of Entanglement

Cited by in corpus (13)

• Stabilizer disentangling of conformal field theories
• Disentangling magic states with classically simulable quantum circuits
• Non-stabilizerness of Neural Quantum States
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Non-Clifford Cost of Random Unitaries
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• Analyzing the free states of one quantum resource theory as resource states of another
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• High-expressibility Quantum Neural Networks using only classical resources
• Adaptively secure unitary designs with constant non-Clifford cost
• Disentangling quantum autoencoder
• Limits of Clifford Disentangling in Tensor Network States